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When studying neural networks from Neural Networks and Learning Machines, by Simon Haykin, the author highlights the close similarity between of adaptive filtering and neural networks.

From a scalar-valued signal, if we put a tapped delay input along with an ADALINE (Adaptive Linear Neuron), do we have an adaptive filter? From this point of view, both areas become closely related.

PS: A good reference is MathWorks - Adaptive Neural Network Filters

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I think adaptive filter, and a single layer perceptron with MSE error, will be equivalent.

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  • $\begingroup$ The main problem imho is that, for adaptive filters, $\mathbf{x}[n] = (x[n], x[n-1], ...)$. It is not necessarily true for neural networks. That is where a tapped delay line comes in. $\endgroup$ Commented May 6, 2023 at 15:54
  • $\begingroup$ Moreover, if we are talking about linear adaptive filtering, a nonlinear activation function prevents they from being equal. That is where ADALINE comes in. $\endgroup$ Commented May 6, 2023 at 15:57
  • $\begingroup$ A single layer perceptron with MSE loss is exactly like adaptive filter as I wrote. You align the samples in batches to match the input. $\endgroup$
    – David
    Commented May 6, 2023 at 18:36

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